Towards all-order factorization of QED amplitudes at next-to-leading power

TL;DR

This paper extends the factorization framework of QED amplitudes to next-to-leading power, introducing universal jet functions and analyzing all-order structures, which advances understanding of gauge-theory amplitudes beyond leading order.

Contribution

It develops an all-order factorization formula for QED amplitudes at NLP, including new jet functions and addressing endpoint divergences, advancing the theoretical framework.

Findings

Reproduces relevant regions in one- and two-loop amplitudes

Introduces universal jet functions at one-loop order

Addresses endpoint divergences and hard-collinear interplay

Abstract

We generalise the factorization of abelian gauge theory amplitudes to next-to-leading power (NLP) in a soft scale expansion, following a recent generalisation for Yukawa theory. From an all-order power counting analysis of leading and next-to-leading regions, we infer the factorized structure for both a parametrically small and zero fermion mass. This requires the introduction of new universal jet functions, for non-radiative and single-radiative QED amplitudes, which we compute at one-loop order. We show that our factorization formula reproduces the relevant regions in one- and two-loop scattering amplitudes, appropriately addressing endpoint divergences. It provides a description of virtual collinear modes and accounts for non-trivial hard-collinear interplay present beyond the one-loop level, making this a first step towards a complete all-order factorization framework for gauge-theory amplitudes at NLP.